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Barabasi links a twenty-first century teenage computer hacker named MafiaBoy to the first century Apostle Paul, and asserts that both were masters of the network.

MafiaBoy - From his bedroom, the teen hacker orchestrated a distributed denial of service attack (DDoS) that was able to crash the websites of some of the biggest names in e-commerce back in the year 2000

A reformed persecutor of Christians had a conversion experience and afterward walked nearly 10,000 miles, over twelve years, spreading the message and faith of a man whom he’d never met

Both mastered the faster and most effective way to reach the largest number of people, each one in its own time. Neither of them fully grasped the forces that aided them in their actions.

Paul and MafiaBoy succeeded because we are all connected

Mapping our interconnectivity

detailed maps of the Internet

companies connected by trade

interactions between specimens and ecosystems

gens working together in a cell

all those diverse maps follow a common blueprint

far-reaching natural laws govern the structure and evolution of all the complex networks that surround us

Reductionism

Reductionism tells us that to comprehend nature, we first must decipher its components, assuming that once we understand the parts it will be easy to understand the whole

It is the wrong approach and has resulted in us taking apart the universe and having no idea how to put it back together

After spending trillions of research dollars to disassemble nature in the last century, we are just now acknowledging that we have no clue how to continue except to take it apart further, because putting it back together turned out to be harder than scientists thought it would be

Complexity

Nature is not a well-designed puzzle with only one way to put it back together and that in complex systems the components can fit in so many different ways that it would take us billions of years to try all the combinations

Nature exploits the laws of self-organization whose roots, he writes, are still largely a mystery

Complexity has a strict architecture. We have come to grasp the importance of networks.

The 'next scientific revolution:the science of networks'

book has a simple aim: to get us to think networks – they are present everywhere and we just need an eye for them

Leonhard Euler in 1736 introduced the idea of graphs and unintentionally created a branch of mathematics known as graph theory, which today is the basis for our thinking about networks

"Euler gave birth to graph theory by replacing each of the four land areas with nodes, and each bridge with a link (4 nodes connected by 7 links)"

Graphs or networks have properties, hidden in their construction, that limit or enhance our ability to do things with them.

The construction and structure of graphs or networks is the key to understanding the complex world around us.

Small changes in the topology, affecting only a few of the nodes or links, can open up hidden doors, allowing new possibilities.

Until the 1950s, the goal of graph theory was simple: discover and catalogue the properties of the various graphs

Paul Erdos and Alfred Renyi - Random Network Theory Model

Paul Erdos and Alfred Renyi together introduced the 'random network theory model'. Random network theory says that nodes in a network connect to each other randomly and, according to Barabasi, it has dominated scientific thinking about networks since being introduced in 1959

Erdos and Renyi never planned to provide a universal theory of network formation. Erdos agreed that networks must have organizing principles that distinguish them from the random network model.

What do real networks look like?

3rd ~ Six Degrees of Separation

Although it would not be given its catchy title until more than sixty years later, the concept was first introduced in 1929 by Hungarian writer Frigyes Karinthy in his short story “Lancszemek” or, in English, “Chains”, which also made it the first time the concept was ever published.

In 1967, Harvard professor Stanley Milgram rediscovered Karinthy’s concept and turned it into a much celebrated and groundbreaking study of our interconnectivity.

Amazing how Milgram's first paper on the subject occasionally read like an English translation of Karinthy's "Chains"

The goal was to find the 'distance' between any two people in the US, sending letters to randomly chosen residents of Wichita and Omaha.

Milgram found that the median number o intermediate person was 5.5, amazingly close to Karinthy's suggestion. But Milgram himself never used the phrase "six degress of separation"

The actual term “six degrees of separation” was not coined until John Guare‘s 1991 stage play of the same title.

Ousa: "Everybody on this planet is separated by only six other people. Six degrees of separation. Between us and everybody else in this planet..."

For Guare's Ousa, six degrees applied to the whole world. Thus a myth was born. More people watch movies than read sociology papers.

Is 'six degrees' something uniquely human? Or do other kinds of networks look the same? Answers surfaced only a few years ago.

By inventing the links in 1980, Tim Berners-Lee released a genie, that in less than 10 years turned into the World Wide Web. Largest ever human-made network.

Links turn the collection of individual documents into a huge network.. the stitches that keep together the fabric or our modern information society together.

Using 'Statistical Mechanics', and focusing on smaller pieces of the web (1k,10k,100k nodes), Barabasi found the separation to be proportional to the logarithm of the number of nodes in the network.

NEC group estimated the size of the public indexable web to be around 800 million nodes at the end of 1998. Diameter=18.59(19)

The natural question is why? How do networks achieve such a uniformly short path despite consisting of billions of nodes?

As we add more links, the distance between nodes suddenly collapses, which can be turned into a formula that predicts separation as a function of the number of nodes.

The origin of the small separation is a logarithmic term present in the formula. The logarithm shrinks the huge networks.

"Small worlds" are a generic property of networks in general. There is a new geometry to master in order to make sense of the complex world around us.

Our society with 6 billion nodes has a separation of 6, the web with close to a billion nodes has a separation of 19, the internet, with thousand of routers has a separation of 10

Karinthy's short story published in 1929, in Budapest

Erdos, also in Budapest, was 17 yrs old

Alfred Renyi, was 9 yrs old, was good friends with Karinthy's son, Ferenc.

Erdos and Renyi in 1959 wrote their famous string of papers on random networks.

Stanley Milgram is a child of Hungarian father and Romanian mother who came to the US and settled in the Bronx

4th ~ Small Worlds

The Strength of Weak Ties - Mark Granovetter - among the most influential, most cited sociology papers ever written

Granovetter proposed that when it comes to finding a job, getting news, launching a restaurant, or spreading the latest fad, our weak social ties are more important that our strong friendships

Interviews: 'Was it a friend? Or just an acquaintance?

An image of a society that is very different from the random universe Erdos and Renyi depicted

Complex networks started to speak to us in a language that scientists trained in self-organization and complexity could finally understand. They spoke of order and emerging behavior.

"There were laws behind complex networks"

3. "How does order emerge from disorder?"

Why do liquids, magnets, and superconductors lose their identity at some critical point and decide to follow identical power laws?

Renormalization: in the vicinity of the critical point, the laws of physics applied in an identical manner at all scales, from single atoms to boxes with millions of identical atoms acting in unison.

We finally learned that when giving birth to order, complex systems divest themselves of their unique features, and display a universal behavior that has similar characteristics in a wide range of systems.

Are real networks in a continuous state of transitions from disorder to order?

Why do hubs appear in networks of all kinds, ranging from actors to the Web?

Why are they described by power laws?

Are there fundamental laws forcing different networks to take up the same universal form and shape?

How does nature spin its webs?

7th ~ Rich Get Richer

Why Hubs? Why Power Laws?

Gathering data from known netwoks

Power grid of the Western United States

C. elegans topology

Hollywood Actor Database

The wiring diagram of a computer chip by IBM

In almost all systems (IBM, actors, power grid) the distribution follows a Power Law

An Insight: Rich-get-Richer phenomenom

Most real networks share an essential feature: GROWTH

growth forces us to rethink our modeling assumptions - networks are not random, not static

It's easy to model a growing network

Model A - We start adding nodes, one after another, and each node has two links.. our 3rd node will link to both of them, the 4th has 3 to chose.

Model A differs from Erdós and Rényi random network model in its growing nature.

Despite the fact of choosing links randomly and democratically, nodes in Model A are not equivalent with each other.

There is a clear advantage for the senior nodes.

The poorest node will be the last one to join the system.

Growth: For each given period of time we add a new node to the network: one node at a time.

The webpages we link to are not ordinary ones - they are HUBS: PREFERENTIAL ATTACHMENT

UNDEMOCRATIC: Hollywood & the WWW force us to abandon the second important inherent assumption inherent in random networks: their democratic character.

Preferential Attachment: We assume that each new node connects to the existing nodes with two links. Given the choice between 2 nodes, one with twice as many links as the other, it is twice as likely that the new node will connect to the more connected node.

As the 1st model to explain the scale-free power laws seen in real networks, it quickly became known as the scale-free model.

Seniority, however, is not sufficient to explain power laws.

Hubs require the help of the second law, preferential attachment

Preferential Attachment induces a rich-get-richer phenomenon

How do latecomers make it in a world in which only the rich get richer?

Could either growth or preferential attachment alone explain the power laws?

The evolution of real networks is far more complex than the scale-free model predicts.

Internal Links: new links emerge spontaneously inside the network, not only when new nodes join it.

Many nodes and links can disappear.

Aging: nodes stop acquiring links after retirement.

Linking to a node would not be simply proportional to the number of links the node has, but would follow some more complicated function.

BUT, in most cases, when GROWTH and PREFERENTIAL ATTACHMENT are simultaneously present, HUBS and POWER LAWS emerge as well.

The scale-free model embodies a new modeling philosophy, by viewing networks as dynamical systems that change continuously over time.

Goals have shifted from describing the topology to understanding the mechanisms that shape network evolution.

Static vs Growing

Random vs Scale-Free

Structure vs Evolution

No matter how large and complex a network becomes, as long as preferential attachment and growth are present, it will maintain its hub-dominated scale-free topology.

9th ~ Achilles' Heel

1996 Failure of the Western Power System

The blackout highlighted an often ignored property of complex networks: vulnerability and interconnectivity

Cascading Failures are a dynamic property of complex systems, a relatively uncharted territory.

The ECOSYSTEM displays a tolerance to erros rarely seen in human-made systems.

Baran's motivation was to build a war-proof system, but in the long run his ideas and innovations were ignored by the military. As a result, the topology of the Internet has little to do with his vision.

The mais objection was to his proposal to break the messages into small packets of uniform size capable of traveling independently of one another along the network. That would need the switch to a digital system, which was not feasible at the time (1964)

The Topology of the Internet is closer to an Ecosystem

Historical forces shaped its topology

The Internet entered the picture around 1965 or 1966, when Bob Taylor (ARPA's Director) decided to somehow link several computers from its research labs around the country.

It suddenly became clear to eferyone that packet switching over faster lines was the technology required to create a truly efficient communication network.

Donald Davies, from British National Physical Lab, reinvented packets and packet switching well before learning of Baran's preexisting work. Presented the concepts in 1967.

And so the Internet was born, and it took a life of its own.

Internet researchers are increasingly morphing from designers into explorers, like biologists or ecologists faced with an incredibly complex system that exists independently of them.

The Internet is comprised of physical lines and routers. It is all hardware. How could it follow the same rules that humans do when establishing their weightless social links or adding URLs to their Webpage?

The MIllenium Map (2000)

No central authority has controlled or documented its grouwth and design.

What neither computer scientists nor biologists know is how the large-scale structure emerges once we put the pieces together.

1999: The Faloutsos Brothers find the connectivity distribution of the Internet routers follows a power law

The discovery meant that all tools used to model the structure of the Internet before 1999, based on ideas rooted in random networks, were simply wrong.

When GROWTH and PREFERENTIAL ATTACHMENT are simultaneously present, HUBS and POWER LAWS emerge as well.

From 1969 to 1972, the Internet grew to 37 nodes, a classic scenario of a growing network - continuing to expand node by node til today.

Preferential Attachment - why would anyone link his or her computer to any router other than the nearest one?

When an institution decides to link its computers to the Internet, the parameter is cost of communication.

Regarding the bandwidth, the closest node is often not the best choice.

Routers offering more bandwidth likely have more links as well.

When chosing a good place to link, we will gravitate toward the more heavily connected access points -- a source of preferential attachment.

Nodes rich in links acquire more links than nodes with a few links only.

The Internet Model:

Growth

Preferential Attachment

Distance Dependence

Underlying Fractal Structure

Each of these forces alone, if taken to the extreme, could destroy the scale-free topology.

This very balance of power is the Internet's own Achilles' heel.

Experts predict that by 2010 there will be around 10.000 telemetric devices for each human on the planet.

There will be soon over 3 billion Internet-connected cell phones and close to 16 billion Internet-connected computers embedded in everything from toasters to fashion designs.

8th ~ Einstein's Legacy

Inktomi: the search engine behind the Web's most popular site Yahoo!, and also the main search engine AltaVista.

June 2000: Yahoo! fires InkTome as its search engine, replacing it with a 2yr-old startup called Google.

Google violated the basic prediction of the scale-free model: that the1st mover has an advantage.

In less than 3 yrs Google became the biggest node and the most popular search engine.

The scale-free model does differentiate between nodes, but on a function of the time of their entry.

The process that separates winners the winners from the losers: competition in complex systems, where each node has a certain FITNESS.

FITNESS is a quantitative measure of a node's ability to stay in front of the competition.

May have genetic roots in people

May be related to product and management quality for companies

Talent for actors

Content for Websites

Your ability to make friends relative to everybody in your neighborhood

A company's competence in luring and keeping consumers

The introduction of FITNESS changes what is considered attractive in a competitive environment

Preferential attachment is driven by the product of the node's fitness and the number of links it has.

If two nodes have the same fitness, however, the older one still has an advantage.

The simple fitness model was 'our' 1st attempt to account for Google

"Our quick fix opened an unexpected window to a rich family of phenomena, that are invisible in a fitness-free universe.

A quest to understand how Google turned into a hub almost overnight. (Ginestra Bianconi)

Fitness is in the driver's seat, making or breaking the hubs

The speed at which nodes acquire links is no longer a matter of seniority: Beauty over Age